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A156181 Number of solutions to e(1)*1 + e(2)*2 + ... + e(n)*n = e(-1)*1 + e(-2)*2 + ... + e(-n)*n, where e(j) are from {-1,0,1}, j=-n,...,n. 8
1, 3, 13, 65, 403, 2669, 18759, 136477, 1020373, 7785741, 60395165, 474817833, 3775005799, 30298719855, 245167429681, 1997854542163, 16381233095985, 135050690760831, 1118800428892925, 9308791880014333, 77755512086256649 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
a(n) = coefficient of x^(n*(n+1)) in the polynomial Product_{k=1..n} (1 + x^k + x^(2*k))^2, and is the maximal such coefficient as well.
LINKS
Ray Chandler, Table of n, a(n) for n = 0..1052 (terms < 10^1000)
Steven R. Finch, Signum equations and extremal coefficients, February 7, 2009. [Cached copy, with permission of the author]
FORMULA
a(n) is the constant term in expansion of Product_{k=1..n} (x^k + 1 + 1/x^k)^2. - Ilya Gutkovskiy, Jan 22 2024
MATHEMATICA
Table[Coefficient[Expand[Product[(1 + x^k + x^(2*k))^2, {k, 1, n}]], x, n*(n + 1)], {n, 0, 20}]
CROSSREFS
Sequence in context: A199143 A002468 A198663 * A260783 A373932 A228987
KEYWORD
nonn
AUTHOR
Steven Finch, Feb 05 2009
STATUS
approved

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Last modified July 17 13:29 EDT 2024. Contains 374377 sequences. (Running on oeis4.)